Three point masses each of mass `m` rotate in a circle of radius `r` with constant angular velocity `omega` due to their mutual gravitational attraction. If at any instant, the masses are on the vertices of an equilateral triangle of side `a`, then the value of `omega` is

Options

A. `sqrt((Gm)/(a^(3)))`
B. `sqrt((3Gm)/(a^(3)))`
C. `sqrt((Gm)/(3a^(3)))`
D. None of these

Answer

B

Explanation

In right angled `DeltaAOB, cos 30^(@)=(OB)/(AB)`
`rArr (sqrt(3))/(2)=(a)/(2r)rArr r=(a)/(sqrt(3))`
`sqrt(3)((Gmm)/(a^(2)))=m(a)/(sqrt(3)).omega^(2)`
`:. omega=sqrt((3Gm)/(a^(3)))`